Multivariate nonparametric techniques for astigmatism analysis

Abstract

Rank-based and sign-based MANOVA had comparable or slightly lower power than the Hotelling T(2) test in detecting differences in normally distributed data. For data sets in which the rectangular components of astigmatism vectors do not distribute normally in both dimensions, only the nonparametric statistical methods were valid. The sign-based MANOVA was the most sensitive in detecting differences in non-normally distributed astigmatism outcomes in the data sets.

Bootstrapping in Applied Linguistics: Assessing its Potential Using Shared Data

“…Their study found virtually no difference between bootstrapped and parametrically-derived descriptives (mean, standard error). Finally, like the two previous studies, the findings of Tongbai et al (2010) do not support the benefits of bootstrapping either. Their study is also the only (quasi-)secondary simulation study we are aware of.…”

“…Further supporting the use of robust statistics described here is the finding that, given a normally distributed dataset, robust statistics such as bootstrapping have been found to approximate their parametric equivalents in power and accuracy; given a non-normal distribution, bootstrapped analyses are much more powerful and therefore more likely to either detect statistical significance when present or to reveal a statistical relationship as spurious (Tukey 1960;Lee and Rogers 1998;Lansing 1999;Wilcox 2001;Larson-Hall and Herrington 2010;Tongbai, Yu, and Miller 2010). A counter argument to the need to employ bootstrapped analyses could be made based on the claim that ANOVA and other means-based analyses are robust to violations of assumptions such as non-normally distributed data, unbalanced Ns, and unequal variance across groups (Lansing 2004;but cf.…”

Dioptric power and refractive behaviour: a review of methods and applications

“…The specific aim below is to relate the analysis of dioptric power using both power vectors and matrices27 and to emphasise a few critical issues also such as departure from normality,21 22 138–141 outliers21 22 and transformations21 22 of data. These important issues are often ignored in analyses 64.…”

“…Although hypothesis tests for dioptric power and refractive behaviour were not included here for the explanatory analysis, means and variance–covariance matrices10 11 can be compared using univariate11 13 15 or multivariate hypothesis tests11–13 15 138–141 and statistical conclusions for refractive behaviour can be made. For example, whether there is a statistically significant difference in means between the right and left eyes or whether the variance–covariance matrices (for example, as in table 1) are equal or not.…”

“…While bivariate CIs are sometimes used24 82 114 130 they are not always applied with due regard to possible outliers and their significance or to the nature of distributions and possible departure from normality 21–23. Consideration of outliers21 22 28 30 31 56–70 73 74 138 and the use of trivariate CIs13 17 18 20–22 24 26 28 30 31 38 39 55–70 73 74 82 that are fundamental to understanding symmetric dioptric power and refractive behaviour are not used as often as necessary. Hypothesis tests are sometimes included in papers but occasionally without due regard to assumptions underlying such statistical tests.…”